Federations simply bring in the sharding pattern into SQL Azure as a first class citizen. Sharding pattern is used for building many of your favorite sites on the web such as social networking sites, auction sites or scalable email applications such as Facebook, eBay and Hotmail. By bringing in the sharding pattern into SQL Azure, federations enable building scalable and elastic database tiers and greatly simplify developing and managing modern multi-tenant cloud applications.
Federations scalability model is something you are already greatly familiar with: Imagine a canonical multi-tier application: these applications scale-out their front and middle tiers for scalability. As the demand on the application varies, administrators add and remove new instances of the front end and middle tier nodes to handle the variance in the workload. With Windows Azure Platform this is easily achieved through easy provisioning of new capacity and the pay as you go model of the cloud. However database tiers have typically not provided support for the same elastic scale-out model. However with federations, SQL Azure enable database tiers to scale-out in a similar model. With federations, database tiers can be elastically scaled-out much like the middle and front tiers of the application based on application workload. Using federations, applications can expand and contract the number of nodes that service the database workload without requiring any downtime!